Robust Calibration of MEMS Accelerometers in the Presence of Outliers

MEMS accelerometers suffer from different problems such as random and systematic errors and the presence of outliers in the measurements. Proper calibration is necessary to obtain accurate results. Various methods exist but very few are designed for robust calibration. This paper explores methods for calibrating MEMS accelerometers in the presence of outliers. Optimization techniques based on Levenberg–Marquardt algorithm and linearization are used to solve the nonlinear calibration equations. Outlier detection methods such as RANSAC (random sample consensus), the Mahalanobis distance, and the median absolute deviation (MAD) are integrated within the optimization algorithm. Outlier scores are calculated and used to eliminate outliers or assign weights. The experimental results show that outlier detection and removal methods allow to achieve substantial improvement in the calibration process compared with non-robust methods. The median absolute deviation is the most effective in detecting outliers. In the presence of outliers, the average error for MAD and model-based method is 0.0136 (a.u.). For non-robust methods, the error is 3.82 (a.u.). For the Mahalanobis distance, the error is 1.8778 (a.u.). The results show that the calibration error is the smallest for the model—based method. The Mahalanobis distance presents higher calibration errors and is less capable of detecting outliers; however, it is still better than non-robust methods. Finally Levenberg–Marquardt algorithm presents slightly better results than linearization.